3x^2+2x=45

Simple and best practice solution for 3x^2+2x=45 equation. Check how easy it is, and learn it for the future. Our solution is simple, and easy to understand, so don`t hesitate to use it as a solution of your homework.

If it's not what You are looking for type in the equation solver your own equation and let us solve it.

Solution for 3x^2+2x=45 equation:


Simplifying
3x2 + 2x = 45

Reorder the terms:
2x + 3x2 = 45

Solving
2x + 3x2 = 45

Solving for variable 'x'.

Reorder the terms:
-45 + 2x + 3x2 = 45 + -45

Combine like terms: 45 + -45 = 0
-45 + 2x + 3x2 = 0

Begin completing the square.  Divide all terms by
3 the coefficient of the squared term: 

Divide each side by '3'.
-15 + 0.6666666667x + x2 = 0

Move the constant term to the right:

Add '15' to each side of the equation.
-15 + 0.6666666667x + 15 + x2 = 0 + 15

Reorder the terms:
-15 + 15 + 0.6666666667x + x2 = 0 + 15

Combine like terms: -15 + 15 = 0
0 + 0.6666666667x + x2 = 0 + 15
0.6666666667x + x2 = 0 + 15

Combine like terms: 0 + 15 = 15
0.6666666667x + x2 = 15

The x term is 0.6666666667x.  Take half its coefficient (0.3333333334).
Square it (0.1111111112) and add it to both sides.

Add '0.1111111112' to each side of the equation.
0.6666666667x + 0.1111111112 + x2 = 15 + 0.1111111112

Reorder the terms:
0.1111111112 + 0.6666666667x + x2 = 15 + 0.1111111112

Combine like terms: 15 + 0.1111111112 = 15.1111111112
0.1111111112 + 0.6666666667x + x2 = 15.1111111112

Factor a perfect square on the left side:
(x + 0.3333333334)(x + 0.3333333334) = 15.1111111112

Calculate the square root of the right side: 3.887301263

Break this problem into two subproblems by setting 
(x + 0.3333333334) equal to 3.887301263 and -3.887301263.

Subproblem 1

x + 0.3333333334 = 3.887301263 Simplifying x + 0.3333333334 = 3.887301263 Reorder the terms: 0.3333333334 + x = 3.887301263 Solving 0.3333333334 + x = 3.887301263 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3333333334' to each side of the equation. 0.3333333334 + -0.3333333334 + x = 3.887301263 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + x = 3.887301263 + -0.3333333334 x = 3.887301263 + -0.3333333334 Combine like terms: 3.887301263 + -0.3333333334 = 3.5539679296 x = 3.5539679296 Simplifying x = 3.5539679296

Subproblem 2

x + 0.3333333334 = -3.887301263 Simplifying x + 0.3333333334 = -3.887301263 Reorder the terms: 0.3333333334 + x = -3.887301263 Solving 0.3333333334 + x = -3.887301263 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3333333334' to each side of the equation. 0.3333333334 + -0.3333333334 + x = -3.887301263 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + x = -3.887301263 + -0.3333333334 x = -3.887301263 + -0.3333333334 Combine like terms: -3.887301263 + -0.3333333334 = -4.2206345964 x = -4.2206345964 Simplifying x = -4.2206345964

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.5539679296, -4.2206345964}

See similar equations:

| a+-19=3 | | x^2+y^2-2sqrt(2)x=z | | 0+f=17 | | 35=-10k-25 | | X^2-5xy-14y^2/x^2+5xy+6y^2 | | 8t-3=2t+1 | | 3m+3=60 | | (-6-4)/(-5) | | y=C(100) | | 5+6j/6+j | | (4x+5)+40=180 | | 3n-6=-9 | | (b+1/b^2-2b+1)-(5-3b/b^2-2b+1) | | 1-(0.5-15.8)=12.8-0.7x | | 12+r=4 | | 8=-12b+5b | | 0=6.28r^2+349.168r-5651.8116 | | 3x+40+4x=180 | | 3+6x(5+4)/3-7=7x | | -1/12+16y+17/12y-19+7/12y | | 5e^3x+1=e^4x | | 17x-6+3x-5=+11+4x | | 4=7y-5y | | 1/6/x=1/9x | | 5x^2+x-20=0 | | -1x+-1=x | | 20x^3+16x^2+8x=0 | | 5(6y-5)=2 | | -20-5(11v+20)=-2(20v-15) | | -19+4d=-3(3d+2) | | P(x)=(x+5)(x-2)(x+3) | | 8=t-1 |

Equations solver categories